Peel and chop the carrots. The pieces do not need to be thin or even. The smaller they are, the faster they soften.
Simmer them with the cashews. In a saucepan, covered with water. You will drain this water later, so there is no need to measure it.
Cook for about 20 minutes. Until a fork slides through the carrots with no resistance at all and the cashews are soft. This step decides the texture: undercooked carrots mean a stringy smoothie, and extra blending will not fix it.
Drain and cool under the tap. Rinse with cold water until everything is completely cold. Never blend anything hot in a sealed blender, because the steam builds pressure.
Add everything to the blender. With the 500 ml (2 cups) of cold water, the sweetener and the pinch of salt.
Blend for at least 2 minutes on high. At the one minute mark it looks done, but it is still gritty. The longer you blend, the silkier it gets.
Strain, if you like. Through a fine mesh strainer or a nut milk bag. You do not need to, since cashews leave almost no pulp, but it makes the texture even smoother.
Serve over ice, or chill and shake before serving. It is much better cold, and separation in the jar is normal.